Determine the general formula and then calculate T10, T15 and T30 for the following sequences:

Question

−21;−27;−33;−39;−45;…

Answer 1

The general formula for this sequence is Tn = -6n - 15.

Calculating T10:
T10 = -6(10) - 15
T10 = -60 - 15
T10 = -75

Calculating T15:
T15 = -6(15) - 15
T15 = -90 - 15
T15 = -105

Calculating T30:
T30 = -6(30) - 15
T30 = -180 - 15
T30 = -195

Therefore, T10 = -75, T15 = -105, and T30 = -195.